Start from clean slate and free up memory

Interstate alliance data

## ── Attaching packages ───────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 3.1.1     ✔ purrr   0.3.2
## ✔ tibble  2.1.1     ✔ dplyr   0.8.1
## ✔ tidyr   0.8.3     ✔ stringr 1.4.0
## ✔ readr   1.1.1     ✔ forcats 0.3.0
## Warning: package 'ggplot2' was built under R version 3.5.2
## Warning: package 'tibble' was built under R version 3.5.2
## Warning: package 'tidyr' was built under R version 3.5.2
## Warning: package 'purrr' was built under R version 3.5.2
## Warning: package 'dplyr' was built under R version 3.5.2
## Warning: package 'stringr' was built under R version 3.5.2
## ── Conflicts ──────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## Loading required package: tergm
## Loading required package: ergm
## Loading required package: network
## Warning: package 'network' was built under R version 3.5.2
## network: Classes for Relational Data
## Version 1.15 created on 2019-04-01.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
##                     Mark S. Handcock, University of California -- Los Angeles
##                     David R. Hunter, Penn State University
##                     Martina Morris, University of Washington
##                     Skye Bender-deMoll, University of Washington
##  For citation information, type citation("network").
##  Type help("network-package") to get started.
## 
## ergm: version 3.9.4, created on 2018-08-15
## Copyright (c) 2018, Mark S. Handcock, University of California -- Los Angeles
##                     David R. Hunter, Penn State University
##                     Carter T. Butts, University of California -- Irvine
##                     Steven M. Goodreau, University of Washington
##                     Pavel N. Krivitsky, University of Wollongong
##                     Martina Morris, University of Washington
##                     with contributions from
##                     Li Wang
##                     Kirk Li, University of Washington
##                     Skye Bender-deMoll, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("ergm").
## NOTE: Versions before 3.6.1 had a bug in the implementation of the
## bd() constriant which distorted the sampled distribution somewhat.
## In addition, Sampson's Monks datasets had mislabeled vertices. See
## the NEWS and the documentation for more details.
## Loading required package: networkDynamic
## 
## networkDynamic: version 0.9.0, created on 2016-01-12
## Copyright (c) 2016, Carter T. Butts, University of California -- Irvine
##                     Ayn Leslie-Cook, University of Washington
##                     Pavel N. Krivitsky, University of Wollongong
##                     Skye Bender-deMoll, University of Washington
##                     with contributions from
##                     Zack Almquist, University of California -- Irvine
##                     David R. Hunter, Penn State University
##                     Li Wang
##                     Kirk Li, University of Washington
##                     Steven M. Goodreau, University of Washington
##                     Jeffrey Horner
##                     Martina Morris, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("networkDynamic").
## 
## tergm: version 3.5.2, created on 2018-08-18
## Copyright (c) 2018, Pavel N. Krivitsky, University of Wollongong
##                     Mark S. Handcock, University of California -- Los Angeles
##                     with contributions from
##                     David R. Hunter, Penn State University
##                     Steven M. Goodreau, University of Washington
##                     Martina Morris, University of Washington
##                     Nicole Bohme Carnegie, New York University
##                     Carter T. Butts, University of California -- Irvine
##                     Ayn Leslie-Cook, University of Washington
##                     Skye Bender-deMoll
##                     Li Wang
##                     Kirk Li, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("tergm").
## Loading required package: ergm.count
## Loading required package: statnet.common
## Warning: package 'statnet.common' was built under R version 3.5.2
## 
## Attaching package: 'statnet.common'
## The following objects are masked from 'package:ergm':
## 
##     colMeans.mcmc.list, sweep.mcmc.list
## The following object is masked from 'package:base':
## 
##     order
## 
## ergm.count: version 3.3.0, created on 2018-08-25
## Copyright (c) 2018, Pavel N. Krivitsky, University of Wollongong
##                     with contributions from
##                     Mark S. Handcock, University of California -- Los Angeles
##                     David R. Hunter, Penn State University
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("ergm.count").
## NOTE: The form of the term 'CMP' has been changed in version 3.2
## of 'ergm.count'. See the news or help('CMP') for more information.
## Loading required package: sna
## sna: Tools for Social Network Analysis
## Version 2.4 created on 2016-07-23.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
##  For citation information, type citation("sna").
##  Type help(package="sna") to get started.
## Loading required package: tsna
## 
## statnet: version 2018.10, created on 2018-10-17
## Copyright (c) 2018, Mark S. Handcock, University of California -- Los Angeles
##                     David R. Hunter, Penn State University
##                     Carter T. Butts, University of California -- Irvine
##                     Steven M. Goodreau, University of Washington
##                     Pavel N. Krivitsky, University of Wollongong
##                     Skye Bender-deMoll
##                     Martina Morris, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("statnet").
## unable to reach CRAN
## [1] "net"    "labels"

Senate Co-Sponsorship data

Campnet data

1 Cohesion, subgroups and communities

## Network attributes:
##   vertices = 18
##   directed = TRUE
##   hyper = FALSE
##   loops = FALSE
##   multiple = FALSE
##   bipartite = FALSE
##  total edges = 54 
##    missing edges = 0 
##    non-missing edges = 54 
##  density = 0.1764706 
## 
## Vertex attributes:
##   vertex.names:
##    character valued attribute
##    18 valid vertex names
## 
## No edge attributes
## 
## Network edgelist matrix:
##       [,1] [,2]
##  [1,]    5    1
##  [2,]    9    1
##  [3,]   12    1
##  [4,]   14    1
##  [5,]   11    2
##  [6,]    5    3
##  [7,]    7    3
##  [8,]    1    4
##  [9,]    3    4
## [10,]    6    4
## [11,]    7    4
## [12,]    8    4
## [13,]    1    5
## [14,]    3    5
## [15,]    6    5
## [16,]    7    5
## [17,]    4    6
## [18,]    5    6
## [19,]    8    6
## [20,]    3    7
## [21,]    4    7
## [22,]    8    7
## [23,]   13    7
## [24,]    4    8
## [25,]    6    8
## [26,]   10    9
## [27,]   12    9
## [28,]   14    9
## [29,]   15    9
## [30,]    2   11
## [31,]   16   11
## [32,]   17   11
## [33,]    1   12
## [34,]    9   12
## [35,]   10   12
## [36,]   14   12
## [37,]    9   14
## [38,]   10   14
## [39,]   12   14
## [40,]   13   15
## [41,]   18   15
## [42,]    2   16
## [43,]   11   16
## [44,]   15   16
## [45,]   17   16
## [46,]   18   16
## [47,]    2   17
## [48,]   11   17
## [49,]   16   17
## [50,]   18   17
## [51,]   13   18
## [52,]   15   18
## [53,]   16   18
## [54,]   17   18

## [1] "Gender"       "na"           "Role"         "vertex.names"
## Network attributes:
##   vertices = 18
##   directed = TRUE
##   hyper = FALSE
##   loops = FALSE
##   multiple = FALSE
##   bipartite = FALSE
##  total edges = 54 
##    missing edges = 0 
##    non-missing edges = 54 
##  density = 0.1764706 
## 
## Vertex attributes:
## 
##  Gender:
##    integer valued attribute
##    18 values
## 
##  Role:
##    integer valued attribute
##    18 values
##   vertex.names:
##    character valued attribute
##    18 valid vertex names
## 
## No edge attributes
## 
## Network edgelist matrix:
##       [,1] [,2]
##  [1,]    5    1
##  [2,]    9    1
##  [3,]   12    1
##  [4,]   14    1
##  [5,]   11    2
##  [6,]    5    3
##  [7,]    7    3
##  [8,]    1    4
##  [9,]    3    4
## [10,]    6    4
## [11,]    7    4
## [12,]    8    4
## [13,]    1    5
## [14,]    3    5
## [15,]    6    5
## [16,]    7    5
## [17,]    4    6
## [18,]    5    6
## [19,]    8    6
## [20,]    3    7
## [21,]    4    7
## [22,]    8    7
## [23,]   13    7
## [24,]    4    8
## [25,]    6    8
## [26,]   10    9
## [27,]   12    9
## [28,]   14    9
## [29,]   15    9
## [30,]    2   11
## [31,]   16   11
## [32,]   17   11
## [33,]    1   12
## [34,]    9   12
## [35,]   10   12
## [36,]   14   12
## [37,]    9   14
## [38,]   10   14
## [39,]   12   14
## [40,]   13   15
## [41,]   18   15
## [42,]    2   16
## [43,]   11   16
## [44,]   15   16
## [45,]   17   16
## [46,]   18   16
## [47,]    2   17
## [48,]   11   17
## [49,]   16   17
## [50,]   18   17
## [51,]   13   18
## [52,]   15   18
## [53,]   16   18
## [54,]   17   18

1.3 Geodesic Distances, Average Distance & Diameter

## $counts
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    1    0    1    1    1    2    1    1    1     0     0     1     0
##  [2,]    2    1    2    2    2    4    2    2    2     0     1     2     0
##  [3,]    1    0    1    1    1    2    1    1    1     0     0     1     0
##  [4,]    2    0    1    1    2    1    1    1    2     0     0     2     0
##  [5,]    1    0    1    3    1    1    1    1    1     0     0     1     0
##  [6,]    1    0    1    1    1    1    2    1    1     0     0     1     0
##  [7,]    1    0    1    1    1    2    1    1    1     0     0     1     0
##  [8,]    2    0    1    1    2    1    1    1    2     0     0     2     0
##  [9,]    1    0    1    1    1    2    1    1    1     0     0     1     0
## [10,]    3    0    3    3    3    6    3    3    1     1     0     1     0
## [11,]    2    1    2    2    2    4    2    2    2     0     1     2     0
## [12,]    1    0    1    1    1    2    1    1    1     0     0     1     0
## [13,]    2    3    1    1    1    2    1    1    1     0     3     1     1
## [14,]    1    0    1    1    1    2    1    1    1     0     0     1     0
## [15,]    1    1    1    1    1    2    1    1    1     0     1     1     0
## [16,]    1    1    1    1    1    2    1    1    1     0     1     1     0
## [17,]    1    1    1    1    1    2    1    1    1     0     1     1     0
## [18,]    1    2    1    1    1    2    1    1    1     0     2     1     0
##       [,14] [,15] [,16] [,17] [,18]
##  [1,]     1     0     0     0     0
##  [2,]     2     2     1     1     2
##  [3,]     1     0     0     0     0
##  [4,]     2     0     0     0     0
##  [5,]     1     0     0     0     0
##  [6,]     1     0     0     0     0
##  [7,]     1     0     0     0     0
##  [8,]     2     0     0     0     0
##  [9,]     1     0     0     0     0
## [10,]     1     0     0     0     0
## [11,]     2     2     1     1     2
## [12,]     1     0     0     0     0
## [13,]     1     1     2     1     1
## [14,]     1     0     0     0     0
## [15,]     1     1     1     2     1
## [16,]     1     1     1     1     1
## [17,]     1     1     1     1     1
## [18,]     1     1     1     1     1
## 
## $gdist
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    0   18    2    1    1    2    2    2    2    18    18     1    18
##  [2,]    5    0    7    6    6    7    7    7    4    18     1     5    18
##  [3,]    2   18    0    1    1    2    1    2    4    18    18     3    18
##  [4,]    3   18    2    0    2    1    1    1    5    18    18     4    18
##  [5,]    1   18    1    2    0    1    2    2    3    18    18     2    18
##  [6,]    2   18    2    1    1    0    2    1    4    18    18     3    18
##  [7,]    2   18    1    1    1    2    0    2    4    18    18     3    18
##  [8,]    3   18    2    1    2    1    1    0    5    18    18     4    18
##  [9,]    1   18    3    2    2    3    3    3    0    18    18     1    18
## [10,]    2   18    4    3    3    4    4    4    1     0    18     1    18
## [11,]    5    1    7    6    6    7    7    7    4    18     0     5    18
## [12,]    1   18    3    2    2    3    3    3    1    18    18     0    18
## [13,]    3    4    2    2    2    3    1    3    2    18     3     3     0
## [14,]    1   18    3    2    2    3    3    3    1    18    18     1    18
## [15,]    2    3    4    3    3    4    4    4    1    18     2     2    18
## [16,]    4    2    6    5    5    6    6    6    3    18     1     4    18
## [17,]    4    2    6    5    5    6    6    6    3    18     1     4    18
## [18,]    3    3    5    4    4    5    5    5    2    18     2     3    18
##       [,14] [,15] [,16] [,17] [,18]
##  [1,]     2    18    18    18    18
##  [2,]     5     3     1     1     2
##  [3,]     4    18    18    18    18
##  [4,]     5    18    18    18    18
##  [5,]     3    18    18    18    18
##  [6,]     4    18    18    18    18
##  [7,]     4    18    18    18    18
##  [8,]     5    18    18    18    18
##  [9,]     1    18    18    18    18
## [10,]     1    18    18    18    18
## [11,]     5     3     1     1     2
## [12,]     1    18    18    18    18
## [13,]     3     1     2     2     1
## [14,]     0    18    18    18    18
## [15,]     2     0     1     2     1
## [16,]     4     2     0     1     1
## [17,]     4     2     1     0     1
## [18,]     3     1     1     1     0
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    0   18    2    1    1    2    2    2    2    18    18     1    18
##  [2,]    5    0    7    6    6    7    7    7    4    18     1     5    18
##  [3,]    2   18    0    1    1    2    1    2    4    18    18     3    18
##  [4,]    3   18    2    0    2    1    1    1    5    18    18     4    18
##  [5,]    1   18    1    2    0    1    2    2    3    18    18     2    18
##  [6,]    2   18    2    1    1    0    2    1    4    18    18     3    18
##  [7,]    2   18    1    1    1    2    0    2    4    18    18     3    18
##  [8,]    3   18    2    1    2    1    1    0    5    18    18     4    18
##  [9,]    1   18    3    2    2    3    3    3    0    18    18     1    18
## [10,]    2   18    4    3    3    4    4    4    1     0    18     1    18
## [11,]    5    1    7    6    6    7    7    7    4    18     0     5    18
## [12,]    1   18    3    2    2    3    3    3    1    18    18     0    18
## [13,]    3    4    2    2    2    3    1    3    2    18     3     3     0
## [14,]    1   18    3    2    2    3    3    3    1    18    18     1    18
## [15,]    2    3    4    3    3    4    4    4    1    18     2     2    18
## [16,]    4    2    6    5    5    6    6    6    3    18     1     4    18
## [17,]    4    2    6    5    5    6    6    6    3    18     1     4    18
## [18,]    3    3    5    4    4    5    5    5    2    18     2     3    18
##       [,14] [,15] [,16] [,17] [,18]
##  [1,]     2    18    18    18    18
##  [2,]     5     3     1     1     2
##  [3,]     4    18    18    18    18
##  [4,]     5    18    18    18    18
##  [5,]     3    18    18    18    18
##  [6,]     4    18    18    18    18
##  [7,]     4    18    18    18    18
##  [8,]     5    18    18    18    18
##  [9,]     1    18    18    18    18
## [10,]     1    18    18    18    18
## [11,]     5     3     1     1     2
## [12,]     1    18    18    18    18
## [13,]     3     1     2     2     1
## [14,]     0    18    18    18    18
## [15,]     2     0     1     2     1
## [16,]     4     2     0     1     1
## [17,]     4     2     1     0     1
## [18,]     3     1     1     1     0
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    1    0    1    1    1    2    1    1    1     0     0     1     0
##  [2,]    2    1    2    2    2    4    2    2    2     0     1     2     0
##  [3,]    1    0    1    1    1    2    1    1    1     0     0     1     0
##  [4,]    2    0    1    1    2    1    1    1    2     0     0     2     0
##  [5,]    1    0    1    3    1    1    1    1    1     0     0     1     0
##  [6,]    1    0    1    1    1    1    2    1    1     0     0     1     0
##  [7,]    1    0    1    1    1    2    1    1    1     0     0     1     0
##  [8,]    2    0    1    1    2    1    1    1    2     0     0     2     0
##  [9,]    1    0    1    1    1    2    1    1    1     0     0     1     0
## [10,]    3    0    3    3    3    6    3    3    1     1     0     1     0
## [11,]    2    1    2    2    2    4    2    2    2     0     1     2     0
## [12,]    1    0    1    1    1    2    1    1    1     0     0     1     0
## [13,]    2    3    1    1    1    2    1    1    1     0     3     1     1
## [14,]    1    0    1    1    1    2    1    1    1     0     0     1     0
## [15,]    1    1    1    1    1    2    1    1    1     0     1     1     0
## [16,]    1    1    1    1    1    2    1    1    1     0     1     1     0
## [17,]    1    1    1    1    1    2    1    1    1     0     1     1     0
## [18,]    1    2    1    1    1    2    1    1    1     0     2     1     0
##       [,14] [,15] [,16] [,17] [,18]
##  [1,]     1     0     0     0     0
##  [2,]     2     2     1     1     2
##  [3,]     1     0     0     0     0
##  [4,]     2     0     0     0     0
##  [5,]     1     0     0     0     0
##  [6,]     1     0     0     0     0
##  [7,]     1     0     0     0     0
##  [8,]     2     0     0     0     0
##  [9,]     1     0     0     0     0
## [10,]     1     0     0     0     0
## [11,]     2     2     1     1     2
## [12,]     1     0     0     0     0
## [13,]     1     1     2     1     1
## [14,]     1     0     0     0     0
## [15,]     1     1     1     2     1
## [16,]     1     1     1     1     1
## [17,]     1     1     1     1     1
## [18,]     1     1     1     1     1
## [1] 2.873786
## [1] 7
## [1] 7

1.4 Components, Component Ratio

## Node 1, Reach 10, Total 10
## Node 2, Reach 16, Total 26
## Node 3, Reach 10, Total 36
## Node 4, Reach 10, Total 46
## Node 5, Reach 10, Total 56
## Node 6, Reach 10, Total 66
## Node 7, Reach 10, Total 76
## Node 8, Reach 10, Total 86
## Node 9, Reach 10, Total 96
## Node 10, Reach 11, Total 107
## Node 11, Reach 16, Total 123
## Node 12, Reach 10, Total 133
## Node 13, Reach 17, Total 150
## Node 14, Reach 10, Total 160
## Node 15, Reach 16, Total 176
## Node 16, Reach 16, Total 192
## Node 17, Reach 16, Total 208
## Node 18, Reach 16, Total 224
## [1] 4
## [1] 1
## Node 1, Reach 10, Total 10
## Node 2, Reach 16, Total 26
## Node 3, Reach 10, Total 36
## Node 4, Reach 10, Total 46
## Node 5, Reach 10, Total 56
## Node 6, Reach 10, Total 66
## Node 7, Reach 10, Total 76
## Node 8, Reach 10, Total 86
## Node 9, Reach 10, Total 96
## Node 10, Reach 11, Total 107
## Node 11, Reach 16, Total 123
## Node 12, Reach 10, Total 133
## Node 13, Reach 17, Total 150
## Node 14, Reach 10, Total 160
## Node 15, Reach 16, Total 176
## Node 16, Reach 16, Total 192
## Node 17, Reach 16, Total 208
## Node 18, Reach 16, Total 224
## [1] 0.2222222
## Node 1, Reach 10, Total 10
## Node 2, Reach 16, Total 26
## Node 3, Reach 10, Total 36
## Node 4, Reach 10, Total 46
## Node 5, Reach 10, Total 56
## Node 6, Reach 10, Total 66
## Node 7, Reach 10, Total 76
## Node 8, Reach 10, Total 86
## Node 9, Reach 10, Total 96
## Node 10, Reach 11, Total 107
## Node 11, Reach 16, Total 123
## Node 12, Reach 10, Total 133
## Node 13, Reach 17, Total 150
## Node 14, Reach 10, Total 160
## Node 15, Reach 16, Total 176
## Node 16, Reach 16, Total 192
## Node 17, Reach 16, Total 208
## Node 18, Reach 16, Total 224
## $membership
##  [1] 1 2 1 1 1 1 1 1 1 3 2 1 4 1 2 2 2 2
## 
## $csize
## [1] 10  6  1  1
## 
## $cdist
##  [1] 2 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0
##  [1] 1 2 1 1 1 1 1 1 1 3 2 1 4 1 2 2 2 2
## [1] 10  6  1  1
##  [1] 2 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0

1.5 Connectivity (Line and Node)

Which nodes in the network, if removed, will increase the number of components we find?

## [1]  1  5 11 12 18
## Node 1, Reach 9, Total 9
## Node 2, Reach 6, Total 15
## Node 3, Reach 6, Total 21
## Node 4, Reach 6, Total 27
## Node 5, Reach 6, Total 33
## Node 6, Reach 6, Total 39
## Node 7, Reach 6, Total 45
## Node 8, Reach 3, Total 48
## Node 9, Reach 4, Total 52
## Node 10, Reach 9, Total 61
## Node 11, Reach 3, Total 64
## Node 12, Reach 16, Total 80
## Node 13, Reach 3, Total 83
## Node 14, Reach 9, Total 92
## Node 15, Reach 9, Total 101
## Node 16, Reach 9, Total 110
## Node 17, Reach 9, Total 119
## [1] 5

1.6 Fragmentation

## [1] 0.6095549
## Node 1, Reach 10, Total 10
## Node 2, Reach 16, Total 26
## Node 3, Reach 10, Total 36
## Node 4, Reach 10, Total 46
## Node 5, Reach 10, Total 56
## Node 6, Reach 10, Total 66
## Node 7, Reach 10, Total 76
## Node 8, Reach 10, Total 86
## Node 9, Reach 10, Total 96
## Node 10, Reach 11, Total 107
## Node 11, Reach 16, Total 123
## Node 12, Reach 10, Total 133
## Node 13, Reach 17, Total 150
## Node 14, Reach 10, Total 160
## Node 15, Reach 16, Total 176
## Node 16, Reach 16, Total 192
## Node 17, Reach 16, Total 208
## Node 18, Reach 16, Total 224

2 Cliques

## $clique.count
##   Agg BRAZEY BILL JOHN ANN CAROL HARRY LEE JENNIE PAULINE BERT DON STEVE
## 1   0      0    0    0   0     0     0   0      0       0    0   0     0
## 2   5      2    0    0   1     2     1   1      0       1    0   0     0
## 3   7      0    0    2   3     1     1   3      2       0    0   0     0
## 4   3      1    1    0   0     0     0   0      0       2    1   1     2
##   PAM PAT RUSS GERY MICHAEL HOLLY
## 1   0   0    0    0       0     0
## 2   1   0    1    0       0     0
## 3   1   0    2    2       1     3
## 4   0   2    0    1       1     0
## 
## $clique.comemb
##         BRAZEY BILL JOHN ANN CAROL HARRY LEE JENNIE PAULINE BERT DON STEVE
## BRAZEY       3    0    0   1     1     0   0      0       1    0   0     1
## BILL         0    1    0   0     0     0   0      0       0    0   1     0
## JOHN         0    0    2   1     1     0   2      0       0    0   0     0
## ANN          1    0    1   4     0     1   2      2       0    0   0     0
## CAROL        1    0    1   0     3     1   1      0       0    0   0     0
## HARRY        0    0    0   1     1     2   0      1       0    0   0     0
## LEE          0    0    2   2     1     0   4      1       0    0   0     0
## JENNIE       0    0    0   2     0     1   1      2       0    0   0     0
## PAULINE      1    0    0   0     0     0   0      0       3    1   0     2
## BERT         0    0    0   0     0     0   0      0       1    1   0     1
## DON          0    1    0   0     0     0   0      0       0    0   1     0
## STEVE        1    0    0   0     0     0   0      0       2    1   0     2
## PAM          0    0    0   0     0     0   1      0       0    0   0     0
## PAT          1    0    0   0     0     0   0      0       2    1   0     2
## RUSS         0    0    0   0     0     0   0      0       1    0   0     0
## GERY         0    1    0   0     0     0   0      0       0    0   1     0
## MICHAEL      0    1    0   0     0     0   0      0       0    0   1     0
## HOLLY        0    0    0   0     0     0   0      0       0    0   0     0
##         PAM PAT RUSS GERY MICHAEL HOLLY
## BRAZEY    0   1    0    0       0     0
## BILL      0   0    0    1       1     0
## JOHN      0   0    0    0       0     0
## ANN       0   0    0    0       0     0
## CAROL     0   0    0    0       0     0
## HARRY     0   0    0    0       0     0
## LEE       1   0    0    0       0     0
## JENNIE    0   0    0    0       0     0
## PAULINE   0   2    1    0       0     0
## BERT      0   1    0    0       0     0
## DON       0   0    0    1       1     0
## STEVE     0   2    0    0       0     0
## PAM       2   0    1    0       0     1
## PAT       0   2    0    0       0     0
## RUSS      1   0    3    1       0     2
## GERY      0   0    1    3       2     2
## MICHAEL   0   0    0    2       2     1
## HOLLY     1   0    2    2       1     3
## 
## $cliques
## $cliques[[1]]
## NULL
## 
## $cliques[[2]]
## $cliques[[2]][[1]]
## [1]  9 15
## 
## $cliques[[2]][[2]]
## [1] 5 6
## 
## $cliques[[2]][[3]]
## [1] 1 5
## 
## $cliques[[2]][[4]]
## [1]  7 13
## 
## $cliques[[2]][[5]]
## [1] 1 4
## 
## 
## $cliques[[3]]
## $cliques[[3]][[1]]
## [1] 15 16 18
## 
## $cliques[[3]][[2]]
## [1] 4 6 8
## 
## $cliques[[3]][[3]]
## [1] 13 15 18
## 
## $cliques[[3]][[4]]
## [1] 4 7 8
## 
## $cliques[[3]][[5]]
## [1] 3 5 7
## 
## $cliques[[3]][[6]]
## [1] 3 4 7
## 
## $cliques[[3]][[7]]
## [1] 16 17 18
## 
## 
## $cliques[[4]]
## $cliques[[4]][[1]]
## [1]  9 10 12 14
## 
## $cliques[[4]][[2]]
## [1]  1  9 12 14
## 
## $cliques[[4]][[3]]
## [1]  2 11 16 17
##   Agg BRAZEY BILL JOHN ANN CAROL HARRY LEE JENNIE PAULINE BERT DON STEVE
## 1   0      0    0    0   0     0     0   0      0       0    0   0     0
## 2   5      2    0    0   1     2     1   1      0       1    0   0     0
## 3   7      0    0    2   3     1     1   3      2       0    0   0     0
## 4   3      1    1    0   0     0     0   0      0       2    1   1     2
##   PAM PAT RUSS GERY MICHAEL HOLLY
## 1   0   0    0    0       0     0
## 2   1   0    1    0       0     0
## 3   1   0    2    2       1     3
## 4   0   2    0    1       1     0
##         BRAZEY BILL JOHN ANN CAROL HARRY LEE JENNIE PAULINE BERT DON STEVE
## BRAZEY       3    0    0   1     1     0   0      0       1    0   0     1
## BILL         0    1    0   0     0     0   0      0       0    0   1     0
## JOHN         0    0    2   1     1     0   2      0       0    0   0     0
## ANN          1    0    1   4     0     1   2      2       0    0   0     0
## CAROL        1    0    1   0     3     1   1      0       0    0   0     0
## HARRY        0    0    0   1     1     2   0      1       0    0   0     0
## LEE          0    0    2   2     1     0   4      1       0    0   0     0
## JENNIE       0    0    0   2     0     1   1      2       0    0   0     0
## PAULINE      1    0    0   0     0     0   0      0       3    1   0     2
## BERT         0    0    0   0     0     0   0      0       1    1   0     1
## DON          0    1    0   0     0     0   0      0       0    0   1     0
## STEVE        1    0    0   0     0     0   0      0       2    1   0     2
## PAM          0    0    0   0     0     0   1      0       0    0   0     0
## PAT          1    0    0   0     0     0   0      0       2    1   0     2
## RUSS         0    0    0   0     0     0   0      0       1    0   0     0
## GERY         0    1    0   0     0     0   0      0       0    0   1     0
## MICHAEL      0    1    0   0     0     0   0      0       0    0   1     0
## HOLLY        0    0    0   0     0     0   0      0       0    0   0     0
##         PAM PAT RUSS GERY MICHAEL HOLLY
## BRAZEY    0   1    0    0       0     0
## BILL      0   0    0    1       1     0
## JOHN      0   0    0    0       0     0
## ANN       0   0    0    0       0     0
## CAROL     0   0    0    0       0     0
## HARRY     0   0    0    0       0     0
## LEE       1   0    0    0       0     0
## JENNIE    0   0    0    0       0     0
## PAULINE   0   2    1    0       0     0
## BERT      0   1    0    0       0     0
## DON       0   0    0    1       1     0
## STEVE     0   2    0    0       0     0
## PAM       2   0    1    0       0     1
## PAT       0   2    0    0       0     0
## RUSS      1   0    3    1       0     2
## GERY      0   0    1    3       2     2
## MICHAEL   0   0    0    2       2     1
## HOLLY     1   0    2    2       1     3
## [[1]]
## NULL
## 
## [[2]]
## [[2]][[1]]
## [1]  9 15
## 
## [[2]][[2]]
## [1] 5 6
## 
## [[2]][[3]]
## [1] 1 5
## 
## [[2]][[4]]
## [1]  7 13
## 
## [[2]][[5]]
## [1] 1 4
## 
## 
## [[3]]
## [[3]][[1]]
## [1] 15 16 18
## 
## [[3]][[2]]
## [1] 4 6 8
## 
## [[3]][[3]]
## [1] 13 15 18
## 
## [[3]][[4]]
## [1] 4 7 8
## 
## [[3]][[5]]
## [1] 3 5 7
## 
## [[3]][[6]]
## [1] 3 4 7
## 
## [[3]][[7]]
## [1] 16 17 18
## 
## 
## [[4]]
## [[4]][[1]]
## [1]  9 10 12 14
## 
## [[4]][[2]]
## [1]  1  9 12 14
## 
## [[4]][[3]]
## [1]  2 11 16 17
## NULL
## [[1]]
## [1]  9 15
## 
## [[2]]
## [1] 5 6
## 
## [[3]]
## [1] 1 5
## 
## [[4]]
## [1]  7 13
## 
## [[5]]
## [1] 1 4
## [[1]]
## [1] 15 16 18
## 
## [[2]]
## [1] 4 6 8
## 
## [[3]]
## [1] 13 15 18
## 
## [[4]]
## [1] 4 7 8
## 
## [[5]]
## [1] 3 5 7
## 
## [[6]]
## [1] 3 4 7
## 
## [[7]]
## [1] 16 17 18
## [[1]]
## [1]  9 10 12 14
## 
## [[2]]
## [1]  1  9 12 14
## 
## [[3]]
## [1]  2 11 16 17

2.1 K-Cores

##  BRAZEY    BILL    JOHN     ANN   CAROL   HARRY     LEE  JENNIE PAULINE 
##       3       3       3       3       3       3       3       3       3 
##    BERT     DON   STEVE     PAM     PAT    RUSS    GERY MICHAEL   HOLLY 
##       3       3       3       3       3       3       3       3       3

2.2 K-cores (new data)

2.3 K-cliques

4 Clustering

4.2 Based on Modularity

\[ \text{Modularity} = \frac{1}{2m}\frac{\sum_{ij}[A_{ij}-k_ik_j]}{2m}1(c_ic_j) \]

where,

  • k is the degree
  • m is the number of edges in the network
  • c is the group index
  • 1 is the indicator function (i.e., are the groups of i and j equal)

5 Key-Players

### Functions

kpp.neg <- function(x,k,n.sim){
  if (length(rownames(x)) == 0) rownames(x) <- c(1:nrow(x))
  if (length(colnames(x)) == 0) colnames(x) <- c(1:ncol(x))
  if (missing(n.sim)) n.sim <- 100
  sims <- array(0, dim=c(n.sim, 2))
  for (sim in 1:n.sim){
  # Populate set S with 3 random nodes, without replacement
  set <- strsplit(sample(colnames(x), k, replace = FALSE, prob = NULL), " ")
  # Remove nodes from network x and calculate F = fit
  matrix <- x[-which(rownames(x) %in% set), -which(colnames(x) %in% set)]
  reciprocal <- matrix(1, nrow(matrix), ncol(matrix))/geodist(matrix)$gdist
  reciprocal[reciprocal==Inf] <- 0
  fit <- 1 - ((2*sum(reciprocal[lower.tri(reciprocal)]))/(nrow(matrix)*(nrow(matrix)-1)))
  non.set <- strsplit(rownames(matrix), " ")
  pairs <- array(0, dim=c(k*length(non.set), 2))
  #colnames(pairs) <- c("Pair", "Delta_F")
  terminate <- FALSE
    while (terminate==FALSE){
      i <- 1
      for (u in set){
        for (v in non.set){
          pairs[i,1] <- paste(set[[which(set %in% u)]],non.set[[which(non.set %in% v)]],sep=',')
          set.new <- set
          set.new[[which(set %in% u)]] <- non.set[[which(non.set %in% v)]]
          matrix <- x[-which(rownames(x) %in% set.new), -which(colnames(x) %in% set.new)]
          reciprocal <- matrix(1, nrow(matrix), ncol(matrix))/geodist(matrix)$gdist
          reciprocal[reciprocal==Inf] <- 0
          fit.new <- 1 - ((2*sum(reciprocal[lower.tri(reciprocal)]))/(nrow(matrix)*(nrow(matrix)-1)))
          delta.fit <- fit.new - fit
          pairs[i,2] <- delta.fit
          i <- i+1
        }
      }
      if (length(pairs[which(as.numeric(pairs[,2]) == max(as.numeric(pairs[,2]))),1])>1){
        all.pairs <- strsplit(pairs[which(as.numeric(pairs[,2]) == max(as.numeric(pairs[,2]))),1], ",") # All pairs that improve fit equally  
        pair.max <- strsplit(sample(all.pairs, 1, replace=FALSE)[[1]], " ")
      } else {pair.max <- strsplit(strsplit(pairs[which(as.numeric(pairs[,2]) == max(as.numeric(pairs[,2]))),1], ",")[[1]]," ")}
      terminate <- max(as.numeric(pairs[,2]))<=0
      if (max(as.numeric(pairs[,2]))>0){ 
          fit <- fit + max(as.numeric(pairs[,2]))
          set[[which(set %in% pair.max)]] <- pair.max[[which(!(pair.max %in% set))]]
          matrix <- x[-which(rownames(x) %in% set), -which(colnames(x) %in% set)]
          non.set <- strsplit(rownames(matrix), " ")
          pairs <- array(0, dim=c(k*length(non.set), 2))
          colnames(pairs) <- c("Pair", "Delta_F")
      }
    }
  output <- data.frame(optimal_set=paste("[",paste(as.character(set), collapse=","),"]", sep=''),
                               max_fragmentation=fit)
  sims[[sim,1]] <- as.character(output$optimal_set)
  sims[[sim,2]] <- output$max_fragmentation
  }
  count <- table(sims[,1][sims[,2]==max(as.numeric(sims[,2]))])
  output <- data.frame(optimal_set=sample(names(count)[count==max(count)], 1, replace=FALSE),
                       max_fragmentation=max(as.numeric(sims[,2])))
  return(output)
}
kpp.pos <- function(x,k,n.sim){
  if (missing(n.sim)) n.sim <- 100
  sims <- array(0, dim=c(n.sim, 4))
  for (sim in 1:n.sim){
    # Sub-function
    colmax <- function(matrix) apply(matrix, 2, max)
    # Main code
    if (length(rownames(x)) == 0) rownames(x) <- c(1:nrow(x))
    if (length(colnames(x)) == 0) colnames(x) <- c(1:ncol(x))
    set <- strsplit(sample(colnames(x), k, replace = FALSE, prob = NULL), " ")
    reciprocal <- matrix(1, nrow(x), ncol(x))/geodist(x)$gdist
    reciprocal[reciprocal==Inf] <- 1
    rownames(reciprocal) <- rownames(x)
    colnames(reciprocal) <- colnames(x)
    non.set <- strsplit(rownames(x[-which(rownames(x) %in% set), -which(colnames(x) %in% set)]), " ")
    fit <- matrix(0,1,3)
    fit[1,1] <- (sum(colmax(reciprocal[which(rownames(reciprocal) %in% set),which(colnames(reciprocal) %in% strsplit(colnames(x), " "))]) ))/ncol(x)
    fit[1,2] <- length(which(colmax(reciprocal[which(rownames(reciprocal) %in% set),which(colnames(reciprocal) %in% strsplit(colnames(x), " "))])==1))
    fit[1,3] <- length(which(colmax(reciprocal[which(rownames(reciprocal) %in% set),which(colnames(reciprocal) %in% strsplit(colnames(x), " "))])>0))/ncol(x)
    #fit.alt <- (sum(colmax(reciprocal[which(rownames(reciprocal) %in% set),which(colnames(reciprocal) %in% non.set)])))/length(non.set)
    pairs <- array(0, dim=c(k*length(non.set), 4))
    terminate <- FALSE
    while (terminate==FALSE){
      i <- 1
      for (u in set){
        for (v in non.set){
          pairs[i,1] <- paste(set[[which(set %in% u)]],non.set[[which(non.set %in% v)]],sep=',')
          set.new <- set
          set.new[[which(set %in% u)]] <- non.set[[which(non.set %in% v)]]
          non.set.new <- non.set
          non.set.new[[which(non.set %in% v)]] <- set[[which(set %in% u)]]
          fit.new <- matrix(0,1,3)
          fit.new[1,1] <- (sum(colmax(reciprocal[which(rownames(reciprocal) %in% set.new),
                                        which(colnames(reciprocal) %in% strsplit(colnames(x), " "))])))/ncol(x)
          fit.new[1,2] <- length(which(colmax(reciprocal[which(rownames(reciprocal) %in% set.new),
                                                    which(colnames(reciprocal) %in% strsplit(colnames(x), " "))])==1))
          fit.new[1,3] <- length(which(colmax(reciprocal[which(rownames(reciprocal) %in% set.new),
                                                    which(colnames(reciprocal) %in% strsplit(colnames(x), " "))])>0))/ncol(x)
          delta.fit <- fit.new[1,1] - fit[1,1]
          pairs[i, 2] <- delta.fit
          pairs[i, 3] <- fit.new[,2]
          pairs[i, 4] <- fit.new[,3]
          i <- i+1
        }
      }
      if (length(pairs[which( as.numeric(pairs[,2]) == max(as.numeric(pairs[,2]))),1]) > 1){ # Do we have multiple optimal pairs?
          all.pairs <- strsplit(pairs[which(as.numeric(pairs[,2]) == max(as.numeric(pairs[,2]))),1], ",") # All pairs that improve fit equally  
          pair.max <- strsplit(sample(all.pairs, 1, replace=FALSE)[[1]], " ")
        } else {pair.max <- strsplit(strsplit(pairs[which(as.numeric(pairs[,2]) == max(as.numeric(pairs[,2]))),1], ",")[[1]]," ")}
        terminate <- max(as.numeric(pairs[,2]))<=0 # terminate if delta.fit <= 0
      if (max(as.numeric(pairs[,2]))>0){ 
            fit[1,1] <- as.numeric(fit[1,1] + max(as.numeric(pairs[,2])))
            fit[1,2] <- as.numeric(pairs[which(pairs[,1] == paste(pair.max, collapse=",")),3])
            fit[1,3] <- as.numeric(pairs[which(pairs[,1] == paste(pair.max, collapse=",")),4])
            set[[which(set %in% pair.max)]] <- pair.max[[which(!(pair.max %in% set))]]
            non.set[[which(non.set %in% pair.max)]] <- pair.max[[which(!(pair.max %in% non.set))]]
            pairs <- array(0, dim=c(k*length(non.set), 4))
            colnames(pairs) <- c("Pair", "Delta_F", "Nodes", "Net_Prop")
        }
    }
  output <- data.frame(optimal_set=paste("[",paste(as.character(set), collapse=","),"]", sep=''),
                               distance_w_reach=fit[,1], nodes = fit[,2], net_prop = fit[,3] )
  sims[[sim,1]] <- as.character(output$optimal_set)
  sims[[sim,2]] <- output$distance_w_reach
  sims[[sim,3]] <- output$nodes
  sims[[sim,4]] <- output$net_prop
  }
  count <- table(sims[,1][sims[,2]==max(as.numeric(sims[,2]))])
  output <- data.frame(optimal_set=sample(names(count)[count==max(count)], 1, replace=FALSE),
                       distance_w_reach=max(as.numeric(sims[,2])), nodes = 0, net_prop = 0)
  output$nodes <- as.numeric(sample(sims[,3][sims[,1] == as.character(output$optimal_set)], 1, replace=FALSE))
  output$net_prop <- as.numeric(sample(sims[,4][sims[,1] == as.character(output$optimal_set)], 1, replace=FALSE))
  return(output)
}

6 Network Hypotheses

Now assume the network is stochastic; We might have hypotheses about the stochastic process:

- Nodes that are similar are likely to form ties: Homophily
- Directed edges are likely to be reciprocated: Reciprocity
- A friend of a friend is a friend: Transitivity

What we have done thus far treats the network as fixed. This distinction defines the traditional divide between social and mathematical sciences approaches to network analysis.

6.1 Continuous Autocorrelation

Autocorrelation is a measure of how much those near to us influence our outcomes. This is easiest to understand in terms of time. Over time, the value of a particular stock - or any other thing of value - is very likely related to the value it held yesterday. We can observe similar situations with respect to physical proximity. The wealth of particular cities can be related to the wealth of the cities that are adjacent to them. Although it is possible for a wealthy city to be adjacent to much poorer cities, it is also likely that any increases in the wealth of a particular city can cause spillovers into neighboring communities. The spillover may not be always be direct, but there is likely to be a relationship there. Network autocorrelation works in much the same way. Though, rather than using physical proximity, network autocorrelation uses network proximity to test whether an individuals’ continuous attributes are related to those of their neighbors. In other words, we can ask quesitons about how a particular attribute appears to be related to the ties within that network. For example: Does wealth attract wealth? Do people with dissimilar wealth tend to form ties? Or, does wealth appear to have little to do with one’s immediate neighborhood?

6.1.1 Moran’s I

Moran’s I ranges from -1 to 1 and is interpreted like Pearson’s Correlation Coefficient.

  • Values approaching -1 indicate negative autocorrelation
  • Values approaching 0 indicate that there is no autocorrelation (independence)
  • Values approaching 1 indicate positive autocorrelation

6.1.2 Geary’s C

Geary’s C ranges from 0 to 2.

  • Values less than 1 indicate positive autocorrelation
  • Values close to 1 indicate that there is no autocorrelation (independence)
  • Values greater than 1 indicate negative autocorrelation

6.3 ERGM

  • Using the Add Health data

## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Stopping at the initial estimate.
## Evaluating log-likelihood at the estimate.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges
## 
## Iterations:  6 out of 20 
## 
## Monte Carlo MLE Results:
##       Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges  -2.7275     0.0591      0  -46.15   <1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 2293  on 4969  degrees of freedom
##  
## AIC: 2295    BIC: 2302    (Smaller is better.)
## [1] 0.06137001
## [1] 0.06136821

## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Stopping at the initial estimate.
## Evaluating log-likelihood at the estimate.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges + nodematch("sex") + nodematch("grade") + nodematch("smokes")
## 
## Iterations:  7 out of 20 
## 
## Monte Carlo MLE Results:
##                  Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges             -4.5787     0.1850      0 -24.752  < 1e-04 ***
## nodematch.sex      0.4621     0.1311      0   3.524 0.000425 ***
## nodematch.grade    3.0493     0.1422      0  21.446  < 1e-04 ***
## nodematch.smokes   0.4062     0.1483      0   2.738 0.006174 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 1712  on 4966  degrees of freedom
##  
## AIC: 1720    BIC: 1746    (Smaller is better.)

## Observed statistic(s) sender4, sender5, sender15, sender17, sender42, sender57, sender63, receiver4, receiver17, and receiver44 are at their smallest attainable values. Their coefficients will be fixed at -Inf.
## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Stopping at the initial estimate.
## Evaluating log-likelihood at the estimate.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges + nodematch("sex") + nodematch("grade") + nodematch("smokes") + 
##     sender + receiver
## 
## Iterations:  7 out of 20 
## 
## Monte Carlo MLE Results:
##                  Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges            -6.54235    1.39273      0  -4.698   <1e-04 ***
## nodematch.sex     0.72340    0.15509      0   4.664   <1e-04 ***
## nodematch.grade   3.60634    0.17189      0  20.981   <1e-04 ***
## nodematch.smokes  1.27256    0.20774      0   6.126   <1e-04 ***
## sender2           2.22577    1.25583      0   1.772   0.0763 .  
## sender3           0.85358    1.31365      0   0.650   0.5158    
## sender4              -Inf    0.00000      0    -Inf   <1e-04 ***
## sender5              -Inf    0.00000      0    -Inf   <1e-04 ***
## sender6           1.17264    1.29221      0   0.907   0.3642    
## sender7           1.82007    1.28618      0   1.415   0.1570    
## sender8           2.33419    1.27155      0   1.836   0.0664 .  
## sender9           2.03254    1.27211      0   1.598   0.1101    
## sender10         -0.12412    1.41704      0  -0.088   0.9302    
## sender11         -0.74302    1.60190      0  -0.464   0.6428    
## sender12         -1.01392    1.57899      0  -0.642   0.5208    
## sender13          1.44915    1.30637      0   1.109   0.2673    
## sender14          1.33064    1.32471      0   1.004   0.3152    
## sender15             -Inf    0.00000      0    -Inf   <1e-04 ***
## sender16          2.34335    1.25453      0   1.868   0.0618 .  
## sender17             -Inf    0.00000      0    -Inf   <1e-04 ***
## sender18          1.99117    1.29061      0   1.543   0.1229    
## sender19         -0.07322    1.40150      0  -0.052   0.9583    
## sender20          1.52207    1.28439      0   1.185   0.2360    
## sender21          2.09979    1.26439      0   1.661   0.0968 .  
## sender22          0.88576    1.34555      0   0.658   0.5104    
## sender23          1.46870    1.28751      0   1.141   0.2540    
## sender24          0.88576    1.34555      0   0.658   0.5104    
## sender25          1.25861    1.34235      0   0.938   0.3484    
## sender26          1.34868    1.27622      0   1.057   0.2906    
## sender27          0.51817    1.35188      0   0.383   0.7015    
## sender28          0.30073    1.35208      0   0.222   0.8240    
## sender29          2.43662    1.28473      0   1.897   0.0579 .  
## sender30          1.36028    1.32210      0   1.029   0.3035    
## sender31          1.88595    1.28043      0   1.473   0.1408    
## sender32          0.72578    1.32209      0   0.549   0.5830    
## sender33          2.09444    1.25897      0   1.664   0.0962 .  
## sender34          2.92916    1.26585      0   2.314   0.0207 *  
## sender35          1.48498    1.28646      0   1.154   0.2484    
## sender36          2.04011    1.27129      0   1.605   0.1085    
## sender37          1.05055    1.32819      0   0.791   0.4290    
## sender38          2.06804    1.28481      0   1.610   0.1075    
## sender39          1.03670    1.40765      0   0.736   0.4614    
## sender40          1.71434    1.26586      0   1.354   0.1756    
## sender41         -0.86750    1.56951      0  -0.553   0.5805    
## sender42             -Inf    0.00000      0    -Inf   <1e-04 ***
## sender43          1.97972    1.28468      0   1.541   0.1233    
## sender44          1.84499    1.28992      0   1.430   0.1526    
## sender45          0.37849    1.35551      0   0.279   0.7801    
## sender46          1.20985    1.30077      0   0.930   0.3523    
## sender47         -0.07322    1.40150      0  -0.052   0.9583    
## sender48          0.83024    1.30801      0   0.635   0.5256    
## sender49          1.82994    1.29996      0   1.408   0.1592    
## sender50          0.39527    1.35435      0   0.292   0.7704    
## sender51          2.59763    1.28047      0   2.029   0.0425 *  
## sender52          2.39671    1.28765      0   1.861   0.0627 .  
## sender53          0.74770    1.30858      0   0.571   0.5677    
## sender54          0.63491    1.34110      0   0.473   0.6359    
## sender55          0.87978    1.41662      0   0.621   0.5346    
## sender56          1.10414    1.30234      0   0.848   0.3965    
## sender57             -Inf    0.00000      0    -Inf   <1e-04 ***
## sender58          2.32900    1.29162      0   1.803   0.0714 .  
## sender59          0.96191    1.31592      0   0.731   0.4648    
## sender60          1.20635    1.29933      0   0.928   0.3532    
## sender61          2.62317    1.27827      0   2.052   0.0402 *  
## sender62         -0.79590    1.57732      0  -0.505   0.6138    
## sender63             -Inf    0.00000      0    -Inf   <1e-04 ***
## sender64          1.37381    1.28712      0   1.067   0.2858    
## sender65          2.34097    1.29990      0   1.801   0.0717 .  
## sender66          2.35099    1.28906      0   1.824   0.0682 .  
## sender67          0.63782    1.41165      0   0.452   0.6514    
## sender68          0.77762    1.32296      0   0.588   0.5567    
## sender69          1.78102    1.27294      0   1.399   0.1618    
## sender70          0.09125    1.43162      0   0.064   0.9492    
## sender71          0.86733    1.45067      0   0.598   0.5499    
## receiver2        -1.43489    1.07362      0  -1.337   0.1814    
## receiver3        -1.69160    1.06305      0  -1.591   0.1115    
## receiver4            -Inf    0.00000      0    -Inf   <1e-04 ***
## receiver5        -0.79045    0.97874      0  -0.808   0.4193    
## receiver6        -1.66543    1.06255      0  -1.567   0.1170    
## receiver7        -0.66723    0.95563      0  -0.698   0.4851    
## receiver8         0.22141    0.91166      0   0.243   0.8081    
## receiver9         0.36172    0.86484      0   0.418   0.6758    
## receiver10       -0.87903    0.95032      0  -0.925   0.3550    
## receiver11       -1.25341    1.00146      0  -1.252   0.2107    
## receiver12       -2.50486    1.27755      0  -1.961   0.0499 *  
## receiver13       -1.65921    1.08480      0  -1.529   0.1261    
## receiver14       -0.19915    0.93421      0  -0.213   0.8312    
## receiver15       -0.21006    0.90663      0  -0.232   0.8168    
## receiver16       -1.03081    0.99540      0  -1.036   0.3004    
## receiver17           -Inf    0.00000      0    -Inf   <1e-04 ***
## receiver18       -1.00664    1.02771      0  -0.979   0.3273    
## receiver19       -0.94528    0.92624      0  -1.021   0.3075    
## receiver20        0.13942    0.88488      0   0.158   0.8748    
## receiver21       -1.59147    1.08360      0  -1.469   0.1419    
## receiver22       -1.73458    1.09012      0  -1.591   0.1116    
## receiver23       -0.12357    0.88993      0  -0.139   0.8896    
## receiver24       -1.73458    1.09012      0  -1.591   0.1116    
## receiver25       -0.42157    0.98180      0  -0.429   0.6676    
## receiver26       -1.22260    0.96921      0  -1.261   0.2072    
## receiver27        0.32993    0.87520      0   0.377   0.7062    
## receiver28       -2.47186    1.27910      0  -1.932   0.0533 .  
## receiver29        0.47522    0.91342      0   0.520   0.6029    
## receiver30        0.12959    0.91004      0   0.142   0.8868    
## receiver31        0.51347    0.87020      0   0.590   0.5551    
## receiver32       -1.66313    1.06639      0  -1.560   0.1189    
## receiver33        0.31993    0.87070      0   0.367   0.7133    
## receiver34        1.66643    0.85103      0   1.958   0.0502 .  
## receiver35        0.12686    0.87443      0   0.145   0.8846    
## receiver36        0.57683    0.85120      0   0.678   0.4980    
## receiver37       -0.54970    0.94518      0  -0.582   0.5608    
## receiver38        0.20867    0.91396      0   0.228   0.8194    
## receiver39       -0.30300    0.98849      0  -0.307   0.7592    
## receiver40       -1.12114    0.97563      0  -1.149   0.2505    
## receiver41       -1.32436    0.96960      0  -1.366   0.1720    
## receiver42        0.75364    0.87979      0   0.857   0.3917    
## receiver43       -0.14799    0.92850      0  -0.159   0.8734    
## receiver44           -Inf    0.00000      0    -Inf   <1e-04 ***
## receiver45       -1.25725    0.99393      0  -1.265   0.2059    
## receiver46       -0.15188    0.90265      0  -0.168   0.8664    
## receiver47       -0.94528    0.92624      0  -1.021   0.3075    
## receiver48       -0.34516    0.87911      0  -0.393   0.6946    
## receiver49       -0.28730    0.97578      0  -0.294   0.7684    
## receiver50       -0.47568    0.91303      0  -0.521   0.6024    
## receiver51        1.82942    0.84156      0   2.174   0.0297 *  
## receiver52        0.59043    0.90601      0   0.652   0.5146    
## receiver53       -1.74439    1.05338      0  -1.656   0.0977 .  
## receiver54        0.41471    0.84789      0   0.489   0.6248    
## receiver55       -1.61996    1.28711      0  -1.259   0.2082    
## receiver56       -1.72440    1.07485      0  -1.604   0.1086    
## receiver57       -1.70193    1.08087      0  -1.575   0.1153    
## receiver58        0.05836    0.94460      0   0.062   0.9507    
## receiver59       -0.63772    0.95194      0  -0.670   0.5029    
## receiver60        0.34174    0.86306      0   0.396   0.6921    
## receiver61        1.19676    0.87435      0   1.369   0.1711    
## receiver62       -1.68211    1.08277      0  -1.554   0.1203    
## receiver63       -0.43936    1.06709      0  -0.412   0.6805    
## receiver64       -2.49890    1.28600      0  -1.943   0.0520 .  
## receiver65       -0.37488    1.01075      0  -0.371   0.7107    
## receiver66        0.68781    0.90364      0   0.761   0.4466    
## receiver67       -0.02045    0.94255      0  -0.022   0.9827    
## receiver68       -0.77370    0.94078      0  -0.822   0.4108    
## receiver69        0.15329    0.88341      0   0.174   0.8622    
## receiver70       -1.75929    1.08335      0  -1.624   0.1044    
## receiver71       -0.47914    1.11343      0  -0.430   0.6670    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 2292  on 4826  degrees of freedom
##  
## AIC: 2580    BIC: 3517    (Smaller is better.) 
## 
##  Warning: The following terms have infinite coefficient estimates:
##   sender4 sender5 sender15 sender17 sender42 sender57 sender63 receiver4 receiver17 receiver44

## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Starting Monte Carlo maximum likelihood estimation (MCMLE):
## Iteration 1 of at most 20:
## Optimizing with step length 0.815023636105832.
## The log-likelihood improved by 3.28.
## Iteration 2 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 0.3939.
## Step length converged once. Increasing MCMC sample size.
## Iteration 3 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 0.04178.
## Step length converged twice. Stopping.
## Finished MCMLE.
## Evaluating log-likelihood at the estimate. Using 20 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .
## This model was fit using MCMC.  To examine model diagnostics and check for degeneracy, use the mcmc.diagnostics() function.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges + nodematch("sex") + nodematch("grade") + nodematch("smokes") + 
##     nodeicov("indegree") + nodeocov("outdegree") + mutual
## 
## Iterations:  3 out of 20 
## 
## Monte Carlo MLE Results:
##                    Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -8.36350    0.38406      0 -21.776   <1e-04 ***
## nodematch.sex       0.53097    0.13152      0   4.037   <1e-04 ***
## nodematch.grade     2.60895    0.16372      0  15.936   <1e-04 ***
## nodematch.smokes    0.87707    0.16218      0   5.408   <1e-04 ***
## nodeicov.indegree   0.29141    0.02938      0   9.918   <1e-04 ***
## nodeocov.outdegree  0.33089    0.03420      0   9.674   <1e-04 ***
## mutual              2.33517    0.23219      0  10.057   <1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 1322  on 4963  degrees of freedom
##  
## AIC: 1336    BIC: 1381    (Smaller is better.)

## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Starting Monte Carlo maximum likelihood estimation (MCMLE):
## Iteration 1 of at most 20:
## Optimizing with step length 0.795084745962182.
## The log-likelihood improved by 2.986.
## Iteration 2 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 0.4863.
## Step length converged once. Increasing MCMC sample size.
## Iteration 3 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 0.04361.
## Step length converged twice. Stopping.
## Finished MCMLE.
## Evaluating log-likelihood at the estimate. Using 20 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .
## This model was fit using MCMC.  To examine model diagnostics and check for degeneracy, use the mcmc.diagnostics() function.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges + nodematch("sex") + nodematch("grade") + nodematch("smokes") + 
##     nodeicov("indegree") + nodeocov("outdegree") + mutual(same = "sex", 
##     diff = TRUE)
## 
## Iterations:  3 out of 20 
## 
## Monte Carlo MLE Results:
##                    Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -8.18804    0.38840      0 -21.081   <1e-04 ***
## nodematch.sex      -0.15083    0.17796      0  -0.848    0.397    
## nodematch.grade     2.83825    0.16214      0  17.505   <1e-04 ***
## nodematch.smokes    0.95409    0.15506      0   6.153   <1e-04 ***
## nodeicov.indegree   0.30766    0.02858      0  10.763   <1e-04 ***
## nodeocov.outdegree  0.34895    0.03465      0  10.071   <1e-04 ***
## mutual.same.sex.1   2.80250    0.38101      0   7.355   <1e-04 ***
## mutual.same.sex.2   2.51012    0.33447      0   7.505   <1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 1340  on 4962  degrees of freedom
##  
## AIC: 1356    BIC: 1408    (Smaller is better.)
## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Starting Monte Carlo maximum likelihood estimation (MCMLE):
## Iteration 1 of at most 2:
## Optimizing with step length 0.490824434226245.
## The log-likelihood improved by 8.98.
## Iteration 2 of at most 2:
## Optimizing with step length 0.
## The log-likelihood improved by < 0.0001.
## MCMLE estimation did not converge after 2 iterations. The estimated coefficients may not be accurate. Estimation may be resumed by passing the coefficients as initial values; see 'init' under ?control.ergm for details.
## Finished MCMLE.
## Evaluating log-likelihood at the estimate. Using 20 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .
## This model was fit using MCMC.  To examine model diagnostics and check for degeneracy, use the mcmc.diagnostics() function.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges + nodematch("sex") + nodematch("grade") + nodematch("smokes") + 
##     nodeicov("indegree") + nodeocov("outdegree") + mutual + triangle
## 
## Iterations:  2 out of 2 
## 
## Monte Carlo MLE Results:
##                     Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -8.447329   0.411812     11 -20.513  < 1e-04 ***
## nodematch.sex       0.695422   0.567867      1   1.225  0.22072    
## nodematch.grade     2.099324   0.726925      1   2.888  0.00388 ** 
## nodematch.smokes    0.779930   0.691021      1   1.129  0.25904    
## nodeicov.indegree   0.277257   0.196627      1   1.410  0.15852    
## nodeocov.outdegree  0.326232   0.177501      1   1.838  0.06607 .  
## mutual              2.414219   0.264785     16   9.118  < 1e-04 ***
## triangle            0.104111   0.001974      5  52.739  < 1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 1348  on 4962  degrees of freedom
##  
## AIC: 1364    BIC: 1416    (Smaller is better.)
## Sample statistics summary:
## 
## Iterations = 16384:1063936
## Thinning interval = 1024 
## Number of chains = 1 
## Sample size per chain = 1024 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                         Mean       SD  Naive SE Time-series SE
## edges                -4287.7   56.985   1.78079        54.7227
## nodematch.sex        -2090.1   26.753   0.83603        23.0149
## nodematch.grade       -604.9    2.069   0.06467         0.6487
## nodematch.smokes     -3011.7   46.767   1.46147        44.8705
## nodeicov.indegree   -18412.3  182.011   5.68784       164.6501
## nodeocov.outdegree  -18510.7  183.198   5.72495       164.6910
## mutual               -2209.4   28.394   0.88732        28.1258
## triangle           -404607.5 7628.479 238.38996      7742.9516
## 
## 2. Quantiles for each variable:
## 
##                         2.5%     25%     50%     75%   97.5%
## edges                -4393.0   -4278   -4256   -4254   -4252
## nodematch.sex        -2140.0   -2086   -2075   -2074   -2072
## nodematch.grade       -609.4    -606    -604    -603    -603
## nodematch.smokes     -3098.0   -3004   -2985   -2984   -2982
## nodeicov.indegree   -18745.0  -18393  -18310  -18301  -18294
## nodeocov.outdegree  -18855.0  -18490  -18409  -18400  -18390
## mutual               -2262.0   -2197   -2193   -2193   -2193
## triangle           -418517.0 -400856 -400285 -400281 -400279
## 
## 
## Sample statistics cross-correlations:
##                        edges nodematch.sex nodematch.grade
## edges              1.0000000     0.9992766       0.8580457
## nodematch.sex      0.9992766     1.0000000       0.8600494
## nodematch.grade    0.8580457     0.8600494       1.0000000
## nodematch.smokes   0.9997922     0.9989568       0.8529524
## nodeicov.indegree  0.9994724     0.9992095       0.8577262
## nodeocov.outdegree 0.9995827     0.9988004       0.8587801
## mutual             0.9967828     0.9950799       0.8496788
## triangle           0.9968457     0.9949700       0.8452099
##                    nodematch.smokes nodeicov.indegree nodeocov.outdegree
## edges                     0.9997922         0.9994724          0.9995827
## nodematch.sex             0.9989568         0.9992095          0.9988004
## nodematch.grade           0.8529524         0.8577262          0.8587801
## nodematch.smokes          1.0000000         0.9992027          0.9992443
## nodeicov.indegree         0.9992027         1.0000000          0.9986497
## nodeocov.outdegree        0.9992443         0.9986497          1.0000000
## mutual                    0.9969793         0.9951137          0.9960971
## triangle                  0.9971082         0.9951650          0.9960478
##                       mutual  triangle
## edges              0.9967828 0.9968457
## nodematch.sex      0.9950799 0.9949700
## nodematch.grade    0.8496788 0.8452099
## nodematch.smokes   0.9969793 0.9971082
## nodeicov.indegree  0.9951137 0.9951650
## nodeocov.outdegree 0.9960971 0.9960478
## mutual             1.0000000 0.9998005
## triangle           0.9998005 1.0000000
## 
## Sample statistics auto-correlation:
## Chain 1 
##              edges nodematch.sex nodematch.grade nodematch.smokes
## Lag 0    1.0000000     1.0000000       1.0000000        1.0000000
## Lag 1024 0.9978822     0.9973618       0.9588703        0.9978785
## Lag 2048 0.9956097     0.9946214       0.9174921        0.9956189
## Lag 3072 0.9932108     0.9918648       0.8849958        0.9932406
## Lag 4096 0.9906572     0.9890740       0.8572930        0.9906926
## Lag 5120 0.9879263     0.9860803       0.8325374        0.9879866
##          nodeicov.indegree nodeocov.outdegree    mutual  triangle
## Lag 0            1.0000000          1.0000000 1.0000000 1.0000000
## Lag 1024         0.9976138          0.9975838 0.9980094 0.9981041
## Lag 2048         0.9951048          0.9950928 0.9959369 0.9960488
## Lag 3072         0.9925363          0.9924803 0.9937697 0.9938370
## Lag 4096         0.9898620          0.9897839 0.9914486 0.9914494
## Lag 5120         0.9870176          0.9869136 0.9889869 0.9889109
## 
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1 
## 
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5 
## 
##              edges      nodematch.sex    nodematch.grade 
##             0.8060             0.8677             2.7930 
##   nodematch.smokes  nodeicov.indegree nodeocov.outdegree 
##             0.7953             0.8363             0.8493 
##             mutual           triangle 
##             0.7576             0.7353 
## 
## Individual P-values (lower = worse):
##              edges      nodematch.sex    nodematch.grade 
##        0.420238633        0.385536607        0.005221836 
##   nodematch.smokes  nodeicov.indegree nodeocov.outdegree 
##        0.426455867        0.403004913        0.395702309 
##             mutual           triangle 
##        0.448679531        0.462131207 
## Joint P-value (lower = worse):  0.9728799 .
## Warning in formals(fun): argument is not a function

## 
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
## Warning: You appear to be calling simulate.ergm() directly. simulate.ergm()
## is a method, and will not be exported in a future version of 'ergm'. Use
## simulate() instead, or getS3method() if absolutely necessary.
## Warning: You appear to be calling simulate.formula() directly.
## simulate.formula() is a method, and will not be exported in a future
## version of 'ergm'. Use simulate() instead, or getS3method() if absolutely
## necessary.

## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Starting Monte Carlo maximum likelihood estimation (MCMLE):
## Iteration 1 of at most 20:
## Optimizing with step length 0.439769576145639.
## The log-likelihood improved by 3.137.
## Iteration 2 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 2.209.
## Step length converged once. Increasing MCMC sample size.
## Iteration 3 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 0.09391.
## Step length converged twice. Stopping.
## Finished MCMLE.
## Evaluating log-likelihood at the estimate. Using 20 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .
## This model was fit using MCMC.  To examine model diagnostics and check for degeneracy, use the mcmc.diagnostics() function.
## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   g ~ edges + nodematch("sex") + nodematch("grade") + nodematch("smokes") + 
##     nodeicov("indegree") + nodeocov("outdegree") + mutual + gwesp
## 
## Iterations:  3 out of 20 
## 
## Monte Carlo MLE Results:
##                    Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -8.04077    0.37598      0 -21.386   <1e-04 ***
## nodematch.sex       0.51263    0.11927      0   4.298   <1e-04 ***
## nodematch.grade     2.18991    0.17145      0  12.773   <1e-04 ***
## nodematch.smokes    0.78448    0.13915      0   5.637   <1e-04 ***
## nodeicov.indegree   0.24020    0.02940      0   8.169   <1e-04 ***
## nodeocov.outdegree  0.27260    0.03537      0   7.708   <1e-04 ***
## mutual              2.06821    0.24307      0   8.509   <1e-04 ***
## gwesp               0.64689    0.15128      0   4.276   <1e-04 ***
## gwesp.decay         0.07613    0.16819      0   0.453    0.651    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 6890  on 4970  degrees of freedom
##  Residual Deviance: 1297  on 4961  degrees of freedom
##  
## AIC: 1315    BIC: 1374    (Smaller is better.)
## Sample statistics summary:
## 
## Iterations = 16384:4209664
## Thinning interval = 1024 
## Number of chains = 1 
## Sample size per chain = 4096 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                       Mean      SD Naive SE Time-series SE
## edges               -4.525  19.030   0.2973         0.9957
## nodematch.sex       -1.023  14.591   0.2280         0.8572
## nodematch.grade     -2.803  14.785   0.2310         0.9135
## nodematch.smokes    -3.635  15.717   0.2456         0.8375
## nodeicov.indegree  -17.785 112.436   1.7568         5.7673
## nodeocov.outdegree -22.485 109.066   1.7042         5.6454
## mutual              -1.917   7.664   0.1197         0.4814
## gwesp               -5.175  22.742   0.3553         1.2982
## gwesp.decay         -2.991  13.736   0.2146         0.8135
## 
## 2. Quantiles for each variable:
## 
##                       2.5%    25%     50%    75%  97.5%
## edges               -41.62 -17.00  -4.000  8.000  33.62
## nodematch.sex       -30.00 -11.00  -1.000  9.000  28.00
## nodematch.grade     -30.00 -13.00  -3.000  7.000  27.00
## nodematch.smokes    -34.00 -14.00  -4.000  7.000  27.00
## nodeicov.indegree  -237.62 -92.00 -16.000 53.000 205.00
## nodeocov.outdegree -239.00 -93.00 -22.000 51.000 195.00
## mutual              -17.00  -7.00  -2.000  3.000  13.00
## gwesp               -48.52 -19.87  -5.566  9.968  40.12
## gwesp.decay         -29.92 -12.19  -3.044  6.279  23.96
## 
## 
## Sample statistics cross-correlations:
##                        edges nodematch.sex nodematch.grade
## edges              1.0000000     0.8005102       0.8247141
## nodematch.sex      0.8005102     1.0000000       0.6253056
## nodematch.grade    0.8247141     0.6253056       1.0000000
## nodematch.smokes   0.8567774     0.6686600       0.7240669
## nodeicov.indegree  0.9302022     0.7428550       0.7006378
## nodeocov.outdegree 0.9527578     0.7427972       0.7428459
## mutual             0.7851500     0.6380697       0.7801156
## gwesp              0.9228793     0.7241971       0.8373366
## gwesp.decay        0.7919423     0.5932845       0.8082424
##                    nodematch.smokes nodeicov.indegree nodeocov.outdegree
## edges                     0.8567774         0.9302022          0.9527578
## nodematch.sex             0.6686600         0.7428550          0.7427972
## nodematch.grade           0.7240669         0.7006378          0.7428459
## nodematch.smokes          1.0000000         0.7345028          0.7772568
## nodeicov.indegree         0.7345028         1.0000000          0.8986153
## nodeocov.outdegree        0.7772568         0.8986153          1.0000000
## mutual                    0.6848388         0.7197478          0.7428481
## gwesp                     0.7802764         0.8778279          0.9000905
## gwesp.decay               0.6718997         0.7611554          0.7829299
##                       mutual     gwesp gwesp.decay
## edges              0.7851500 0.9228793   0.7919423
## nodematch.sex      0.6380697 0.7241971   0.5932845
## nodematch.grade    0.7801156 0.8373366   0.8082424
## nodematch.smokes   0.6848388 0.7802764   0.6718997
## nodeicov.indegree  0.7197478 0.8778279   0.7611554
## nodeocov.outdegree 0.7428481 0.9000905   0.7829299
## mutual             1.0000000 0.8162420   0.7640932
## gwesp              0.8162420 1.0000000   0.8727561
## gwesp.decay        0.7640932 0.8727561   1.0000000
## 
## Sample statistics auto-correlation:
## Chain 1 
##              edges nodematch.sex nodematch.grade nodematch.smokes
## Lag 0    1.0000000     1.0000000       1.0000000        1.0000000
## Lag 1024 0.7269258     0.7361147       0.8195312        0.7226876
## Lag 2048 0.5829042     0.5983578       0.7019531        0.5770559
## Lag 3072 0.4947217     0.5179058       0.6068046        0.4938609
## Lag 4096 0.4394357     0.4639378       0.5457865        0.4378630
## Lag 5120 0.3872358     0.4139731       0.4935546        0.3836537
##          nodeicov.indegree nodeocov.outdegree    mutual     gwesp
## Lag 0            1.0000000          1.0000000 1.0000000 1.0000000
## Lag 1024         0.7207850          0.7259825 0.8326302 0.7717094
## Lag 2048         0.5719512          0.5823544 0.7193619 0.6481079
## Lag 3072         0.4867342          0.4903281 0.6297919 0.5649531
## Lag 4096         0.4278588          0.4310962 0.5612675 0.5089659
## Lag 5120         0.3751412          0.3801334 0.4970629 0.4523930
##          gwesp.decay
## Lag 0      1.0000000
## Lag 1024   0.7727372
## Lag 2048   0.6475194
## Lag 3072   0.5631358
## Lag 4096   0.5010415
## Lag 5120   0.4502251
## 
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1 
## 
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5 
## 
##              edges      nodematch.sex    nodematch.grade 
##            -0.5564            -0.6961            -0.5742 
##   nodematch.smokes  nodeicov.indegree nodeocov.outdegree 
##            -0.2424            -0.6078            -0.4281 
##             mutual              gwesp        gwesp.decay 
##            -0.5744            -0.6288            -0.7071 
## 
## Individual P-values (lower = worse):
##              edges      nodematch.sex    nodematch.grade 
##          0.5779188          0.4863770          0.5658610 
##   nodematch.smokes  nodeicov.indegree nodeocov.outdegree 
##          0.8084409          0.5433314          0.6685615 
##             mutual              gwesp        gwesp.decay 
##          0.5656642          0.5294929          0.4794825 
## Joint P-value (lower = worse):  0.9413868 .
## Warning in formals(fun): argument is not a function

## 
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).

## 
## Goodness-of-fit for in-degree 
## 
##    obs min mean max MC p-value
## 0    3   4 8.26  15       0.00
## 1    4   4 8.16  16       0.08
## 2   15   2 8.79  17       0.04
## 3   11   3 9.28  17       0.50
## 4   10   3 8.17  14       0.60
## 5    4   1 6.40  14       0.44
## 6    9   1 5.25  10       0.10
## 7    6   0 4.03  11       0.48
## 8    5   0 3.69   9       0.56
## 9    1   0 3.03   7       0.32
## 10   1   0 2.03   5       0.70
## 11   1   0 1.25   4       1.00
## 12   1   0 0.91   3       1.00
## 13   0   0 0.51   2       1.00
## 14   0   0 0.35   3       1.00
## 15   0   0 0.32   2       1.00
## 16   0   0 0.11   1       1.00
## 17   0   0 0.16   2       1.00
## 18   0   0 0.15   2       1.00
## 19   0   0 0.08   1       1.00
## 20   0   0 0.03   1       1.00
## 21   0   0 0.03   1       1.00
## 23   0   0 0.01   1       1.00
## 
## Goodness-of-fit for out-degree 
## 
##    obs min mean max MC p-value
## 0    7   5 9.88  15       0.38
## 1    5   2 7.31  15       0.46
## 2    8   2 8.28  15       1.00
## 3    7   2 7.59  13       1.00
## 4    9   3 7.43  14       0.54
## 5    9   1 7.21  14       0.62
## 6   12   1 6.04  10       0.00
## 7    6   1 5.03  10       0.76
## 8    5   0 3.72   9       0.58
## 9    2   0 2.99   7       0.72
## 10   1   0 1.89   5       0.82
## 11   0   0 1.12   5       0.64
## 12   0   0 0.76   3       0.92
## 13   0   0 0.65   3       1.00
## 14   0   0 0.47   2       1.00
## 15   0   0 0.23   2       1.00
## 16   0   0 0.18   1       1.00
## 17   0   0 0.09   2       1.00
## 18   0   0 0.08   1       1.00
## 19   0   0 0.01   1       1.00
## 20   0   0 0.03   1       1.00
## 23   0   0 0.01   1       1.00
## 
## Goodness-of-fit for edgewise shared partner 
## 
##       obs min  mean max MC p-value
## esp0   64  43 61.64  82       0.80
## esp1   96  62 95.20 127       0.98
## esp2   63  51 68.03  92       0.68
## esp3   54  24 42.40  66       0.20
## esp4   16   6 22.10  41       0.38
## esp5    9   1 10.36  21       0.84
## esp6    1   0  4.14   9       0.12
## esp7    2   0  1.55   6       0.92
## esp8    0   0  0.55   4       1.00
## esp9    0   0  0.16   1       1.00
## esp10   0   0  0.09   1       1.00
## 
## Goodness-of-fit for minimum geodesic distance 
## 
##     obs min    mean  max MC p-value
## 1   305 254  306.22  349       0.94
## 2   606 639  886.24 1133       0.00
## 3   840 856 1290.84 1578       0.00
## 4   863 595  856.21 1144       1.00
## 5   639  62  281.74  531       0.00
## 6   414   2   60.14  237       0.00
## 7   244   0   10.70  119       0.00
## 8   182   0    1.48   53       0.00
## 9   112   0    0.09    4       0.00
## 10   51   0    0.00    0       0.00
## 11   28   0    0.00    0       0.00
## 12    5   0    0.00    0       0.00
## Inf 681 678 1276.34 1995       0.02
## 
## Goodness-of-fit for model statistics 
## 
##                     obs  min    mean  max MC p-value
## edges               305  254  306.22  349       0.94
## nodematch.sex       180  148  179.07  226       1.00
## nodematch.grade     233  193  234.80  267       0.82
## nodematch.smokes    230  198  229.51  275       0.98
## nodeicov.indegree  1807 1522 1821.48 2072       0.84
## nodeocov.outdegree 1777 1514 1786.96 2058       0.98
## mutual               85   67   85.70  104       1.00
## esp#1                96   62   95.20  127       0.98
## esp#2                63   51   68.03   92       0.68
## esp#3                54   24   42.40   66       0.20
## esp#4                16    6   22.10   41       0.38
## esp#5                 9    1   10.36   21       0.84
## esp#6                 1    0    4.14    9       0.12
## esp#7                 2    0    1.55    6       0.92
## esp#8                 0    0    0.55    4       1.00
## esp#9                 0    0    0.16    1       1.00
## esp#10                0    0    0.09    1       1.00